Controllable double optical bistability via photon and phonon interaction in a hybrid optomechanical system

The optical bistability have been studied theoretically in a multi-mode optomechanical system with two mechanical oscillators independently coupled to two cavities in addition to direct tunnel coupling between cavities. It is proved that the bistable behavior of mean intracavity photon number in the right cavity can be tuned by adjusting the strength of the pump laser beam driving the left cavity. And the mean intracavity photon number is relatively larger in the red sideband regime than that in the blue sideband regime. Moreover, we have shown that the double optical bistability of intracavity photon in the right cavity and the two steady-state positions of mechanical resonators can be observed when the control field power is increased to a critical value. Besides, the critical values for observing bistability and double bistability can be tuned by adjusting the coupling coefficient between two cavities and the coupling rates between cavities mode and mechanical mode.